Trump administration officials say there will be no more conditions imposed on North Korea before a first-ever meeting of the two nation’s leaders beyond the North’s promise not to resume nuclear testing and missile flights or publicly criticize U.S.-South Korean military exercises.

The officials’ comments March 11 followed the surprise announcement last week that President Donald Trump has agreed to meet the North’s Kim Jong Un by May.

“This potential meeting has been agreed to, there are no additional conditions being stipulated, but, again they—they cannot engage in missile testing, they cannot engage in nuclear testing and they can’t publicly object to the U.S.-South Korea planned military exercises,” deputy White House spokesman Raj Shah said.

Treasury Secretary Steven Mnuchin said the summit would give President Trump a chance “to sit down and see if he can cut a deal” with Mr. Kim over the North’s nuclear program. “The president has been very clear in what the objective is here. And that is to get rid of nuclear weapons on the [Korean] peninsula,” Mr. Mnuchin said.

The administration officials credited toughened economic sanctions imposed by the United Nations, and pushed by the United States, with helping bring Mr. Kim to the brink of negotiations.

“Our policy is pressure, is pressure from our partners and allies around the world, pressure to the United Nations, pressure through China, these have had an impact. It’s impacted Kim Jong Un’s behavior. It’s impacted his conduct,” Mr. Shah said.

But some members of Congress said they worry that Mr. Trump acted impulsively in agreeing to meet with Mr. Kim, before negotiators for both countries had a chance to set some goals the leaders could agree to.

“But the important thing is the diplomatic work that has to go in before such a meeting. A meeting like that would be kind of an afterthought after things are negotiated. Here it looks as if, you know, that’s kind of the opening gambit. And that’s a little worrisome,” said Senator Jeff Flake, a Republican of Arizona.

The U.S. and South Korea hold military maneuvers every year. They were postponed during the recent Winter Olympics in South Korea. They are expected to be held in April, but no official announcement has been made about when they will take place. In an interview en route to the Middle East, Defense Secretary Jim Mattis declined to discuss the timing and scale of the exercises.

Secretary Mattis would not talk at all about the diplomatic push over North Korea’s nuclear program. “When you get in a position like this, the potential for misunderstanding remains very high,” he said.

Mr. Mattis was among the advisers in the White House on March 8 when Mr. Trump decided to accept Mr. Kim’s offer to meet. The offer was relayed to Mr. Trump by a South Korean government delegation that briefed the president on their meeting with Mr. Kim last week in North Korea’s capital.

Mr. Trump said on March 10 that he believes North Korea will abide by its pledge to suspend missile tests while he prepares for the summit. He noted in a tweet that North Korea has refrained from such tests since November and said Mr. Kim “has promised not to do so through our meetings.”

“I believe they will honor that commitment,” the president said.

Later, at a political rally in Pennsylvania, when Mr. Trump mentioned Mr. Kim’s name, the crowd booed. But Mr. Trump responded: “No, it’s very positive…no, after the meeting you may do that, but now we have to be very nice because let’s see what happens, let’s see what happens.”